Question: Emily is 20 years older than Luis. Emily and Luis first met 3 years ago. Eighteen years ago, Emily was 5 times older than Luis. How old is Emily now?
Answer: We can use the given information to write down two equations that describe the ages of Emily and Luis. Let Emily's current age be $e$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $e = l + 20$ Eighteen years ago, Emily was $e - 18$ years old, and Luis was $l - 18$ years old. The information in the second sentence can be expressed in the following equation: $e - 18 = 5(l - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $e$ , it might be easiest to solve our first equation for $l$ and substitute it into our second equation. Solving our first equation for $l$ , we get: $l = e - 20$ . Substituting this into our second equation, we get the equation: $e - 18 = 5($ $(e - 20)$ $ -$ $ 18)$ which combines the information about $e$ from both of our original equations. Simplifying the right side of this equation, we get: $e - 18 = 5e - 190$ Solving for $e$ , we get: $4 e = 172$ $e = 43$.